Numerical simulation for computational modelling of reaction–diffusion Brusselator model arising in chemical processes

2018 ◽  
Vol 57 (1) ◽  
pp. 149-179 ◽  
Author(s):  
Sanjay Kumar ◽  
Ram Jiwari ◽  
R. C. Mittal
Keyword(s):  
Numerical Simulation ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Chemical Processes ◽  
Brusselator Model

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

Shape Optimization and Strength Evaluation of Metal Welded Bellows Wave of Mechanical Seal

2008 ◽  
Vol 33-37 ◽  
pp. 1377-1382 ◽  
Author(s):  
Halida Musha ◽  
Mamtimin Gheni ◽  
Buhalqam
Keyword(s):  
Numerical Simulation ◽  
Bone Mass ◽  
Boundary Conditions ◽  
Shape Optimization ◽  
Reaction Diffusion ◽  
Mechanical Seal ◽  
Forming Process ◽  
Strength Evaluation ◽  
Fem Method ◽  
Initial Load

In this paper, the iBone (Imitation Bone) model which is coupled with Turing reaction-diffusion system and FEM, is used. The numerical simulation of bone forming process by considering the osteoclasts and osteoblasts process are conducted. The bone mass is increased with increase of the initial load value, then fibula and femur bones are obtained respectively by keeping the required bone forming value. The new S shape wave of metal welded bellow of mechanical seal are designed based on the the optimization results through this method. The S shape and V shape both were analyzed with FEM method. The same boundary conditions were given for two types of wave. The results are shown that the stresses mainly concentrated on the welded area. It is interesting that the value of the stresses of the two types of wave basically same. However, compressibility of the two types of wave is very different at the same computation stage. The compressibility of S shape wave was higher than V shape.

Design of an Air-Cooled Radial Turbine: Part 1 — Computational Modelling

2018 ◽  
Author(s):  
Yang Zhang ◽  
Tomasz Duda ◽  
James A. Scobie ◽  
Carl M. Sangan ◽  
Colin D. Copeland ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Experimental Testing ◽  
Temperature Drop ◽  
Computational Modelling ◽  
Operating Conditions ◽  
Inlet Temperature ◽  
Topology Optimisation ◽  
Internal Cooling ◽  
Element Analysis ◽  
Radial Turbine

This paper is part of a two-part publication that aims to design, simulate and test an internally air cooled radial turbine. To achieve this, the additive manufacturing process, Selective Laser Melting (SLM), was utilized to allow internal cooling passages within the blades and hub. This is, to the authors’ knowledge, the first publication in the open literature to demonstrate an SLM manufactured, cooled concept applied to a small radial turbine. In this paper, the internally cooled radial turbine was investigated using a Conjugate Heat Transfer (CHT) numerical simulation. Topology Optimisation was also implemented to understand the areas of the wheel that could be used safely for cooling. In addition, the aerodynamic loss and efficiency of the design was compared to a baseline non-cooled wheel. The experimental work is detailed in Part 2 of this two-part publication. Given that the aim was to test the rotor under representative operating conditions, the material properties were provided by the SLM technology collaborator. The boundary conditions for the numerical simulation were derived from the experimental testing where the inlet temperature was set to 1023 K. A polyhedral unstructured mesh made the meshing of internal coolant plenums including the detailed supporting structures possible. The simulation demonstrated that the highest temperature at the blade leading edge was 117 K lower than the uncooled turbine. The coolant mass flow required by turbine was 2.5% of the mainstream flow to achieve this temperature drop. The inertia of the turbine was also reduced by 20% due to the removal of mass required for the internal coolant plenums. The fluid fields in both the coolant channels and downstream of the cooled rotor were analyzed to determine the aerodynamic influence on the temperature distribution. Furthermore, the solid stress distribution inside the rotor was analyzed using Finite Element Analysis (FEA) coupled with the CFD results.

scholarly journals Stationary localized structures and the effect of the delayed feedback in the Brusselator model

2018 ◽  
Vol 376 (2135) ◽  
pp. 20170385 ◽  
Author(s):  
B. Kostet ◽  
M. Tlidi ◽  
F. Tabbert ◽  
T. Frohoff-Hülsmann ◽  
S. V. Gurevich ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Delayed Feedback ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Delayed Feedback Control ◽  
Brusselator Model ◽  
Localized Structures ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions

The Brusselator reaction–diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

A BGK MODEL FOR CHEMICAL PROCESSES: THE REACTION-DIFFUSION APPROXIMATION

1994 ◽  
Vol 04 (01) ◽  
pp. 35-47 ◽  
Author(s):  
RENATO SPIGLER ◽  
DAMIÁN H. ZANETTE
Keyword(s):  
Kinetic Model ◽  
Diffusion Approximation ◽  
Reaction Diffusion ◽  
Chemical Processes ◽  
Reaction Diffusion Equations ◽  
The Other ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Chemical Substances ◽  
Chemical Effects

A BGK-type kinetic model is derived for describing the interaction of chemical substances. The ensuing equation is then solved asymptotically on certain space-time scales on which an appreciable interplay between kinetic and chemical effects, or the prevailing of one on the other, can be observed. The description of the interaction at the macroscopic level consists of a hierarchy of reaction-diffusion equations satisfied by the densities. Comparison is made with similar results previously obtained from certain phenomenological models, and illustrative examples are given.

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